Hello!
I got this wrong in my review because I was using と. Is it wrong to use と or is it actually acceptable?
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で is the correct particle here because と is only used to connect nouns.
While the English translation appears to be doing that, it’s actually two sentences linked together:
- He was an American mathematician.
- He was a university professor.
The use of ‘and’ here is to connect the two sentences.
In Japanese you use て-forms of words to do the same thing. After な-adjectives and nouns it’s で instead. See the lesson on Adjective + て・Noun + で (JLPT N5) | Bunpro which has a similar example using で after a noun.
Imabi also has a very similar example to the sentence you posted (The Particle と I – IMABI 今日):
14a. 私は日本人と医者です X
14b. 私は日本人で 医者です。 〇
I am Japanese and a doctor.
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Thanks for the response, @Gymea . I should’ve included the lesson that Bunpro associated with the sentence which is this Adjective + て + B (JLPT N5) | Bunpro
And the と lesson that I was applying: と (JLPT N5) | Bunpro
So while I understand those 2 lessons, I’m still wondering if と is acceptable in the example.
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No, we cannot use と in the Quentin sentence either. To try to rephrase Gymea’s perfect explanation, the difference is really in whether two separate nouns are linked and then one action happens involving both of them, versus two separate actions.
クエンティンさんは映画監督です would be the first “action” or state of being, and クエンティンさんは俳優です is the second one, so と cannot connect them.
The lesson you linked mentions in passing that で used here is pretty much である. You could without change of meaning say something like クエンティンさんは映画監督でありながら俳優でもある (I hope I’m not butchering it offhand).
In contrast, you can use と in a construction like this: クエンティンさんは映画監督と俳優をやっています, where instead of state-of-beings these become just normal nouns, and the action is instead that Quentin is employed/acting in the capacity of both director and actor at the same time.
Hope this helps
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Thanks for the explanation, @casual
“the difference is really in whether two separate nouns are linked and then one action happens involving both of them, versus two separate actions.” >> This makes sense but I, being not a linguist, can’t un-see the 2 nouns. 
“In contrast, you can use と in a construction like this: クエンティンさんは映画監督と俳優をやっています, where instead of state-of-beings these become just normal nouns, and the action is instead that Quentin is employed/acting in the capacity of both director and actor at the same time.” >>> This makes it clearer but doesn’t make it easier to remember, not because of the quality of the explanation but because of previous wiring in the brain. 
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